The EMS Publishing House is now EMS Press and has its new home at ems.press.
Please find all EMS Press journals and articles on the new platform.
Revista Matemática Iberoamericana
Full-Text PDF (438 KB) | Metadata |
Table of Contents | RMI summary
Published online: 2019-05-09
Polynomial bounds for automorphisms groups of foliations
Maurício Corrêa[1] and Alan Muniz[2] (1) Universidade Federal de Minas Gerais, Belo Horizonte, Brazil(2) Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
Let $(X, \mathcal{F})$ be a foliated surface and $G$ a finite group of automorphisms of $X$ that preserves $\mathcal{F}$. We investigate invariant loci for $G$ and obtain upper bounds for its order that depends polynomially on the Chern numbers of $X$ and $\mathcal{F}$. As a consequence, we estimate the order of the automorphism group of some foliations under mild restrictions. We obtain an optimal bound for foliations on the projective plane which is attained by the automorphism groups of the Jouanolou's foliations.
Keywords: Automorphism, holomorphic foliations
Corrêa Maurício, Muniz Alan: Polynomial bounds for automorphisms groups of foliations. Rev. Mat. Iberoam. 35 (2019), 1153-1194. doi: 10.4171/rmi/1081